Integrating Using Arctan

1. Feb 1, 2009

jumbogala

1. The problem statement, all variables and given/known data
Integrate
1/(x2 +11x +29)

2. Relevant equations

3. The attempt at a solution
I'm doing something wrong, but can't figure out what...

Complete the square so that the denominator equals (x+2)2+25

Then divide by 25: ((x+2)2)/25 + 1

Move that 25 into the squared part: ((x+2)/5)2+1

Substitute the squared part for u.

Find du/dx = 1/5, and therefore 5du=dx

Now we have 5*(integral sign) du / (u2+1)

This gives 5arctan(u)+C --> substitute u back for what you had before.

But the answer is 1/5arctan(u). Where did I go wrong?

Last edited: Feb 1, 2009
2. Feb 1, 2009

NoMoreExams

When you "divide by 25", where does that 25 go?

3. Feb 1, 2009

jumbogala

Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

Thanks!

4. Feb 1, 2009

Dick

You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?

5. Feb 2, 2009

djeitnstine

how about x+2 = 5tanu to make life easier